Daily budget

It might help if you give us some parameters as to what you consider a realistic way to travel / live.

Some people are happy in shared bunk rooms in a hostel while others need a suite at the Ritz.

What do want to do (activity wise) and how do you want to travel / live while you're in Israel?

I'm a backpacker, I want to see the sites. I don't do dorms but like cheap and cheerful, don't mind roughing it a little. Local transport is cool etc

I suggest that you avoid Israel during the Passover holiday - April 6 to 14. The country will be packed with tourists and many Israelis take the entire week off for family vacations in the country. The result - all tourist sites are crowded, traffic jams, full hostels and high prices. You will enjoy your visit a lot more if you delay it for a week.

The youth hostels in Israel have private rooms and are open to everyone:
http://www.iyha.org.il
There are many private hostels in the larger cities that you can find with a Google search. For example this one in Tel-Aviv is in an excellent location:
http://www.hayarkon48.com/

In general, Israel is not a cheap country like its neighbours and prices are equivalent to western Europe. There is an excellent selection of street food at reasonable prices - falaffel, shwarma, pizza, hummus, etc. You can go into supermarkets and buy prepared meats and salads and make your own sandwiches. Public transport is cheap. For example the bus from T-A to Jerusalem (60 km, about 1 hr) costs only 20 NIS.

For room and board - you're coming during high season - places like Jerusalem around Easter may be a tight sqeeze to find a room, and very costly... But you should plan that ahead and see what prices you come up.
If the budget is tight - try and base yourself in an East Jerusalem hostel - you'll have great access to Tel Aviv by service taxi, and good access to Jericho, Ramallah, Bethlehem, the Dead Sea and Masada.

Apart for that, and very roughly:
You're coming for a short time, which means a lot of transportation in a short time and moving around a bit.

Consider about NIS80-100 per day for transport
and about NIS 80-150 a day for food (very basic)

Entry into national parks such as Masada is between 20-40NIS

Ok so 100 per day for transport.
150 per day for food.
accommodation is how much?
And what is this approx in Euros or dollars?
Many thanks

250 shekels is about €50.

A dorm bed is usually around €20. I think it would be tough to find a private single for less than €40-50. So it looks like you should budget around €100 a day.

Further to what has already been written, take a look at FAQ 51 to see how the Passover holiday will affect your trip.

The chances of finding ANY accommodation within your budget at this short notice is virtually nil, with the possible exception of somewhere in east (Arab) Jerusalem if you're very lucky. Most places were booked up months ago. Passover is absolutely peak travel time, with prices to match. National parks such as Masada will be crammed wall-to-wall with families. Roads will be jam packed, and public transport swamped. In short, your dates are not exactly the best time to visit, and especially at such short notice.